In this paper, we essentially finish the classification of those finite 2, 3-groups G having integral group rings with the multiplicative Jordan decomposition (MJD) property. If G is abelian or a Hamiltonian 2-group, then it is clear that Z[G] satisfies MJD. Thus, we need only consider the nonabelian case. Recall that the 2-groups with MJD were completely determined by Hales, Passi and Wilson, ...

A fast Discrete Cosine Transform (DCT) algorithm is introduced that can be of particular interest in image processing. The main features of the algorithm are regularity of the graph and very low arithmetic complexity. The 16-point version of the algorithm requires only 32 multiplications and 81 additions. The computational core of the algorithm consists of only 17 nontrivial multiplications, th...

We reformulate the proof of the renormalization of a spontaneously broken gauge theory by multiplicatively renormalizing the vacuum expectation value of the Higgs field in the SU(2) Higgs model. After BRST symmetry was discovered [1], it was noted that the renormalization of gauge theories [2] can be simplified by using BRST methods. In [3] Becchi, Rouet and Stora considered the SU(2) Higgs mod...

We thank Dr. VanderWeele for his thoughtful addition (1) to our analysis of the interactions between coinfecting enteric pathogens (2). We appreciate the generalizability of his framework that allows the relaxation of the assumption of monotonicity. Here, we consider the importance of the biology to the monotonicity assumption, causal inference, and the scale on which mechanistic interaction is...

We thank Dr. VanderWeele for his thoughtful addition (1) to our analysis of the interactions between coinfecting enteric pathogens (2). We appreciate the generalizability of his framework that allows the relaxation of the assumption of monotonicity. Here, we consider the importance of the biology to the monotonicity assumption, causal inference, and the scale on which mechanistic interaction is...

Let M be a matroid without loops or coloops and let TM be its Tutte polynomial. In 1999 Merino and Welsh conjectured that max(TM (2, 0), TM (0, 2)) ≥ TM (1, 1) for graphic matroids. Ten years later, Conde and Merino proposed a multiplicative version of the conjecture which implies the original one. In this paper we show the validity of the multiplicative conjecture when M is a lattice path matr...

Scalable TCP [2] is a proposition for a new TCP where both the increase and the decrease rate of the window size are multiplicative. It has been recently proposed in order to improve performance in high speed networks. In this paper, we present a mathematical analysis of such multiplicative increase multiplicative decrease protocols in the presence of random losses. These are typical to wireles...

The author considers a special kind of B-product which is called the multiplicative B-product. The most important property of multiplicative B-product is that it preserves multiplicativity of functions. In the previous work [1], the author showed a new kind of convolution product called the B-product defined as follows. For every natural number n let Bn be the set of some pairs (r, s) of diviso...

Let G be a connected graph. The multiplicative Zagreb eccentricity indices of G are defined respectively as Π1(G) = ∏ v∈V (G) ε 2 G(v) and Π ∗ 2(G) = ∏ uv∈E(G) εG(u)εG(v), where εG(v) is the eccentricity of vertex v in graph G and εG(v) = (εG(v)) . In this paper, we present some bounds of the multiplicative Zagreb eccentricity indices of Cartesian product graphs by means of some invariants of t...